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"in full generality" is a correct and usable phrase in written English.
You can use it to talk about something that is considered in its full scope, context, and breadth. For example: "This solution solves the problem in full generality."
Exact(42)
Both men used coordinates to develop notations that expressed the ideas of calculus in full generality and led naturally to differentiation rules and the fundamental theorem of calculus (connecting differential and integral calculus).
Here, -independence is proved in full generality.
We state our main result in full generality.
When we state the decision-theoretic norms in question, we state them in full generality.
If they did, we would be able to prove Cantor's theorem in full generality.
In this paper we consider relationships in full generality, conveniently represented by pedigrees.
Similar(18)
The notion of a scheme itself, however a notion which, if considered in its full generality, generalizes not only the notion of a group but also the notion of a Moore geometry and that of a building in the sense of Jacques Tits–has been considered as the subject of an abstract theory in itself only relatively recently.
(Lewis 1992a: 108) That means that while there may be a convention of truthfulness and trust in L*, there is no convention of trust in L in its full generality.
To the best of our knowledge, the result has not been established in its full generality yet for any generalized differential equation.
Solving the problem of in vivo parameter estimation in its full generality will require meeting a number of additional challenges.
However, solving the M-S functional in its full generality is an overkill in many vision applications.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com